Finite Math Examples

$μ = 100$ , $σ = 15$ , $x = 75$

Step 1

The z-score converts a non-standard distribution to a standard distribution in order to find the probability of an event.

$\frac{x - μ}{σ}$

Step 2

Find the z-score.

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Step 2.1

Fill in the known values.

$\frac{75 - (100)}{15}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Cancel the common factor of $75 - (100)$ and $15$ .

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Step 2.2.1.1

Rewrite $75$ as $- 1 (- 75)$ .

$\frac{- 1 (- 75) - (100)}{15}$

Step 2.2.1.2

Factor $- 1$ out of $- 1 (- 75) - (100)$ .

$\frac{- 1 (- 75 + 100)}{15}$

Step 2.2.1.3

Factor $5$ out of $- 1 (- 75 + 100)$ .

$\frac{5 (- 1 (- 15 + 20))}{15}$

Step 2.2.1.4

Cancel the common factors.

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Step 2.2.1.4.1

Factor $5$ out of $15$ .

$\frac{5 (- 1 (- 15 + 20))}{5 (3)}$

Step 2.2.1.4.2

Cancel the common factor.

$\frac{5 (- 1 (- 15 + 20))}{5 \cdot 3}$

Step 2.2.1.4.3

Rewrite the expression.

$\frac{- 1 (- 15 + 20)}{3}$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Add $- 15$ and $20$ .

$\frac{- 1 \cdot 5}{3}$

Step 2.2.2.2

Multiply $- 1$ by $5$ .

$\frac{- 5}{3}$

Step 2.2.2.3

Move the negative in front of the fraction.

$- \frac{5}{3}$